We all know the story of Benedict Arnold, but were there also instances where high-level British Officers became sympathetic enough to the cause of American independence, that they switched sides and betrayed the King?

Unless I'm overlooking someone, there is no British counterpart of similar rank or who committed a betrayal to the extent of Benedict Arnold during the war. There were certainly former British officers among the patriots, but they had aligned themselves early in the war. No doubt there were low-ranking soldiers here and there who defected, but no high ranking British officers switched sides after the early part of the war.

The main reason behind this, other than the simple fact that most people had made up their minds if they were going to support the rebellion or not by the time the war broke out, is illustrated with the only person I can think of who comes close to what you're looking for, former British officer [Charles Lee](http://en.wikipedia.org/wiki/Charles_Lee_(general)). Lee moved to America in 1773 and resigned his commission when hostilities broke out. He wanted to be put in charge of the Continental army, but unlike Washington, he wanted to be compensated. By aligning himself with the rebels, he was forfeiting all of his land in England, which was a pretty big sacrifice. It was a lot to ask someone to give up all of their land in England in order to fight for American Independence, so they had a lot to lose by switching to the side of the colonists. Lee's service is rather checkered after that, with some claims that he was a traitor to the American cause later in the war, but the fact remains, most British officers weren't willing to make that sacrifice.

That being said, there are instances of British generals who may have been sympathetic to the cause and either resigned their commands or were recalled after British leadership became disappointed in their performance. Some people back in Britain believed they were traitors, though it was not to the extent of Arnold's treachery, and was at most an unwillingness to continue fighting the rebels or exasperation with British leadership and lack of support from back home. Such claims have been leveled at many British generals in the war such as Thomas Gage, William Howe, and even Charles Cornwallis, with varying support to back up the claims.

Though not an officer, nor an all out traitor, perhaps also notable along with this question is the former British Prime Minister, William Pitt, who became very popular in America after he vocally supported the colonists and their grievances that had caused the war and stated in 1777, before the House of Lords that:

"I know that the conquest of English America is an impossibility. You cannot, I venture to say it, you CANNOT conquer America...As to conquest, therefore, my Lords, I repeat, it is impossible. You may swell every expense, and every effort, still more extravagantly; pile and accumulate every assistance you can buy or borrow; traffic and barter with every little pitiful German Prince, that sells and sends his subjects to the shambles of a foreign country; your efforts are for ever vain and impotent—doubly so from this mercenary aid on which you rely; for it irritates, to an incurable resentment, the minds of your enemies—to overrun them with the sordid sons of rapine and plunder; devoting them and their possessions to the rapacity of hireling cruelty! If I were an American, as I am an Englishman, while a foreign troop was landed in my country, I never would lay down my arms, never! never! never! ...I call upon the honour of your Lordships to reverence the dignity of your ancestors, and to maintain your own. I call upon the spirit and humanity of my country to vindicate the national character. I invoke the genius of the constitution. From the tapestry that adorns these walls, the immortal ancestor of this noble Lord frowns with indignation at THE DISGRACE OF HIS COUNTRY! In vain he led your victorious fleets against the boasted Armada of Spain; in vain he defended and established the honour, the liberties, the religion, the Protestant religion of his country, against the arbitrary cruelties of Popery and the Inquisition."

edit: grammar typo